Simplify (5a-2b)(5a+2b)

$(5 a - 2 b) (5 a + 2 b)$

Step 1

Expand $(5 a - 2 b) (5 a + 2 b)$ using the FOIL Method.

Apply the distributive property.

$5 a (5 a + 2 b) - 2 b (5 a + 2 b)$

Apply the distributive property.

$5 a (5 a) + 5 a (2 b) - 2 b (5 a + 2 b)$

Apply the distributive property.

$5 a (5 a) + 5 a (2 b) - 2 b (5 a) - 2 b (2 b)$

Step 2

Simplify terms.

Combine the opposite terms in $5 a (5 a) + 5 a (2 b) - 2 b (5 a) - 2 b (2 b)$ .

Reorder the factors in the terms $5 a (2 b)$ and $- 2 b (5 a)$ .

$5 a (5 a) + 2 \cdot 5 a b - 2 \cdot 5 a b - 2 b (2 b)$

Subtract $2 \cdot 5 a b$ from $2 \cdot 5 a b$ .

$5 a (5 a) + 0 - 2 b (2 b)$

Add $5 a (5 a)$ and $0$ .

$5 a (5 a) - 2 b (2 b)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a - 2 b (2 b)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 \cdot 5 (a \cdot a) - 2 b (2 b)$

Multiply $a$ by $a$ .

$5 \cdot 5 a^{2} - 2 b (2 b)$

Multiply $5$ by $5$ .

$25 a^{2} - 2 b (2 b)$

Rewrite using the commutative property of multiplication.

$25 a^{2} - 2 \cdot 2 b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$25 a^{2} - 2 \cdot 2 (b \cdot b)$

Multiply $b$ by $b$ .

$25 a^{2} - 2 \cdot 2 b^{2}$

Multiply $- 2$ by $2$ .

$25 a^{2} - 4 b^{2}$